Question

Joselyn is a manager at a sign-painting company. She has two painters, Allen and Brianne. Allen can complete a large project in 16 hours. Brianne can complete the project in 18 hours. Joselyn wants to know how long it will take them to complete the project together.

Write an equation and solve for the time it takes Allen and Brianne to complete the project together. Explain each step.

Answer 1

Let area to be painted = X m²

Rate for Allen = X / 16 m² / h

Rate for Brianne = X / 18 m² / h

Combined rate

X/16 + X/18 m² / h

[ 18X + 16X ] / 144 m² / h

34 X / 144 m² / h

time = X / [ 34 X / 144 ] h

time = 144 / 34 h

time = 4 h 14 min